An \alpha-particle and a proton of the same kinetic energy are in turn allowed to pass through a magnetic field \overrightarrow{B}, acting normal to the direction of motion of the particles. Calculate the ratio of radii of the circular paths described by them.

CBSE Class 12 Physics 2019 Delhi Set 1 Paper - Question 8

Question : 8 of 27

Marks: +1, -0

α

-particle and a proton of the same kinetic energy are in turn allowed to pass through a magnetic field

{B}↖{→}

, acting normal to the direction of motion of the particles. Calculate the ratio of radii of the circular paths described by them.

Solution:

Formula
Calculation of ratio of radii

\;\text " radius "\; r=\;{m v}/{q B}=\;{{√{2 m k}}}/{q B}

K_a=K_{\;\text "proton "\;}

M_a=4 m_p

q_a=2 q_p

\;{r_α}/{r_p}=\; {{√{2 m_α K}}/{q_α B}}/ {√{2 m_p K} /{{q_p B} } }

=√{\;{m_α}/{m_p}} × \;{q_p}/{q_α}

={√{4}} × \;{1}/{2}=1

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